The hair dryer plug is usually not really a GFCI, it is an immersion detector. There is a ring in the barrel of the blower exhaust that is connected via the 3d wire to the plug and it looks for current on that wire. (at least in the ones I have taken apart).
I have no clue as to why a 7w lamp would affect that. Do you have another dryer you can try in the same outlet?
